TSTP Solution File: GRP067-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP067-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:15:28 EDT 2023
% Result : Unsatisfiable 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 38 ( 25 unt; 9 typ; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
divide: ( $i * $i ) > $i ).
tff(decl_23,type,
identity: $i ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
inverse: $i > $i ).
tff(decl_26,type,
a1: $i ).
tff(decl_27,type,
a2: $i ).
tff(decl_28,type,
a3: $i ).
tff(decl_29,type,
b3: $i ).
tff(decl_30,type,
c3: $i ).
cnf(single_axiom,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(divide(identity,divide(X1,identity)),X2) = divide(divide(identity,X1),X2),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(divide(identity,divide(identity,divide(X1,divide(identity,X2)))),X2) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
divide(identity,divide(X1,identity)) = divide(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_7]) ).
cnf(c_0_11,plain,
divide(divide(identity,divide(identity,X1)),identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_10]) ).
cnf(c_0_12,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_11]),c_0_6]),c_0_6]) ).
cnf(c_0_13,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
prove_these_axioms ).
cnf(c_0_15,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_16,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_17,plain,
divide(identity,divide(X1,divide(X2,divide(identity,X1)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_12]),c_0_12]) ).
cnf(c_0_18,plain,
divide(divide(X1,divide(identity,X2)),X2) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( divide(identity,divide(identity,a2)) != a2
| divide(divide(identity,a1),divide(identity,a1)) != identity
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),divide(divide(identity,X3),X4))))) = divide(divide(identity,divide(X3,X2)),X4),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_21,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_6])]) ).
cnf(c_0_23,plain,
divide(divide(X1,divide(divide(identity,X2),divide(divide(identity,X3),X4))),X2) = divide(divide(X1,X3),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_13])]) ).
cnf(c_0_25,plain,
divide(X1,divide(X2,divide(identity,X3))) = divide(divide(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_6]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(rw,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_27,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP067-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:15:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.008000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------